Generalized Ince Gaussian beams
- Others:
- Dickey, Fred M.
- Shealy, David L.
Abstract
In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.
Additional Information
© 2006 Society of Photo-Optical Instrumentation Engineers (SPIE). This research was supported by Tecnológico de Monterrey (grant CAT-007) and by Consejo Nacional de Ciencia y Tecnología (grant 42808). M. A. Bandres acknowledge support from Secretaría de Educación Pública de México.Attached Files
Published - 62900S.pdf
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Additional details
- Eprint ID
- 99705
- Resolver ID
- CaltechAUTHORS:20191106-141757099
- CAT-007
- Tecnológico de Monterrey
- 42808
- Consejo Nacional de Ciencia y Tecnología (CONACYT)
- Secretaría de Educación Pública de México
- Created
-
2019-11-06Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Series Name
- Proceedings of SPIE
- Series Volume or Issue Number
- 6290